Question

incorrect
2 tries left. please try again.
∠e and ∠f are complementary. the measure of ∠e is 54° more than the measure of ∠f. find the measure of each angle.
m∠f =
m∠e =

Explanation:

Step1: Define variables and relationship

Let \( m\angle F = x \). Then \( m\angle E = x + 54^\circ \). Since \( \angle E \) and \( \angle F \) are complementary, \( m\angle E + m\angle F = 90^\circ \).

Step2: Substitute and solve for \( x \)

Substitute \( m\angle E \) and \( m\angle F \) into the complementary angle equation: \( x + (x + 54^\circ) = 90^\circ \). Simplify: \( 2x + 54^\circ = 90^\circ \). Subtract \( 54^\circ \) from both sides: \( 2x = 90^\circ - 54^\circ = 36^\circ \). Divide by 2: \( x = \frac{36^\circ}{2} = 18^\circ \). So \( m\angle F = 18^\circ \) and \( m\angle E = 18^\circ + 54^\circ = 72^\circ \).

Answer:

\( m\angle F = 18^\circ \), \( m\angle E = 72^\circ \)